We consider system of hyperbolic balance laws governing relativistic two-fluid flow in which entropy is produced only by disequilibrium between the temperatures of the fluids. We compare two such models: one in which thermal equilibrium is attained through a relaxation procedure, and a fully relaxed model. We describe how the relaxation procedure may be made consistent with the second law of thermodynamics. The wave velocities for both models are obtained and compared: the mixture hydrodynamical velocity of the relaxed system is always less than the hydrodynamical velocity of the relaxation system.
We consider a two-constituent model of a relativistic superfluid. Making use of the singular surface theory, we find the velocities of first and second sounds, due only to the particle number density current n and the entropy current s, respectively. Applying the second-order compatibility conditions, we are able to determine the discontinuities associated to the two waves and the transport equations for the amplitude of the discontinuities. Finally, plane, cylindrical and spherical waves are also investigated.
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